Well, there aren't too many things I would bet my life on, but I'm pretty certain about that.

I don't think injury has anything to do with it.

If the starter allows the first batter to reach base and then leaves the because of an injury, and his team goes on to lose 15-0, the starter is still the loser.

If a SP leaves a game with his team trailing, regardless of when, and his team never ties the score or goes ahead, the SP is the losing pitcher.

The official scorer does, however, have the option of awarding a win at his discretion, though.

Let's say the home is trailing 2-0 after three innings. A relief pitcher comes in in the 4th, and gives up 3 more runs, so it's now 5-0 going to the bottom of the 4th.

In the bottom of the 4th, the home team pinch hits for the reliever, scores 6 runs, and takes the lead, 6-5.

Those 6 runs belong to the relief pitcher, and if the home team goes on to win without ever giving up the lead, he is technically entitled to the win.

But if a second reliever comes in and finishes the game, and shuts out the visiting team for the 5th thru the 9th, or pitches 2 or 3 shutout innings or allows only one or two runs, the official scorer may, at his discretion, award the win to the second reliever because the first one did not pitch effectively, even though he left the game on the winning side of the ledger.